A secret gem on the block is The Institute of the American Musical.
Miles Kreuger has been collecting everything about American musical theatre for many years and has one of the most extensive collections in the world. Check out the scanned brochure (50MB pdf)
You can see him walking his dog, Jenny. When you see him, you should say hi and ask to see the amazing collection, or you can call.
121 N Detroit St
Los Angeles CA 90036